Path integral for a neutral spinning particle in interaction with a rotating magnetic field and a scalar potential

In this paper we consider a neutral spinning particle in interaction with a linear increasing rotating magnetic field and a scalar harmonic potential using the path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger’s model. The calculations are carried out explicitly using fermionic exterior current sources. The problem is then reduced to that of a spinning forced harmonic particle whose spin is coupled to exterior derivative current sources. The result of the propagator is given as a series which is exactly summed up by means of the Laplace transformation and the use of some recurrence formula of the oscillator wave functions. The energy spectrum and the corresponding wave functions are also deduced.